After selecting your membership category, and proceeding to the next page, there are two boxes next to the Relationships section, within the Additional member cards/guest passes section. The two boxes are Is Child and Request Card. You want to know if it's possible to hide the Is Child or Request Card checkbox from this section.
The Is Child and Request Card checkboxes are enabled by default when the option for "Allow members to specify the names and relationships of additional members" is marked under the Membership Form part section: Membership Category>Cards/Guest pass details.
In order to remove these checkboxes, you would have to remove the option to Allow member to specify the names and relationships of additional members.
If you want to keep Allow member to specify the names and relationships of additional members enabled, in order to hide the checkboxes, a customization written by a web developer would need to be written. How do I fix make changes to the design on my site?